I know you don't want to piece your back, but if you have to you can use the John Flynn method for piecing the back. This is my go to method if I can't find the fabric I want in the width I want (for your quilt you could use the 108" backing fabric or even 90" backing fabric) and with a single diagonal seam you can have a back that is wide enough. Because this is on the diagonal, it seems to miss most of the seams on the front. I use the calculator (the first link) to determine how much fabric I need. I could not bring up John Flynn's actual site, but these links give a lot of good information.
Here are some links:
http://www.multi-patch.com/html/diag...calculator.php
https://bsue.wordpress.com/2007/03/2...ng-directions/
http://kristaquilts.blogspot.com/201...d-backing.html